Stationary stochastic signal

The following sections arc organized as follows. Section 18.3 deals with an ysis of deterministic and stationary stochastic signals. Analysis of nonstationary signals is discussed in Sec. 18.4. Sub-... 

An important feature of a process signal is its periodicity, or, in other words, its frequency content. Fourier theory indicates that it is possible to separate individual frequency components from stationary signals (i.e., stochastic signals whose statistical characteristics do not change over time) and make a transformation from the amplitude-time domain to the amplitude-frequency domain. This transformation is known as the Fourier Transform (FT). The Fourier transform of a continuous stationary signal z t) for a given frequency to in radians is defined as. 

The performance of various rectification methods is compared for the noise-free underlying signal represented as a uniform distribution, non-stationary stochastic process, and data with deterministic features. 

A treatment in the frequency domain is not always optimal. For instance, calculations with non-stationary stochastic processes are difficult. Moreover, the PSD is mostly determined by Fourier transforming the ACF, therefore an expression using directly the ACF avoids Fourier transforming. The derivation happens to be not difficult. Assuming a random signal n(t) with mean value y, we write the random variable ... 

A stochastic process is termed stationary, if the signal generating process is time invariant. All distributions and statistical parameters of a stationary process are independent of time. A process varying with time is called nonstationary. 

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